Ditsy,
Mitford Street was in Elswick suburb of Newcastle ( Yes, Ok, still within the wider district of Westgate)
What about Stephen's Gateshead-born son, William ?. He was also a landscape painter. And he was advertised within Trade Directories of the period ... and went "up-market" to Coxlodge, Gosforth ( C1881 5096-77-15)
e.g.
Whellans Directory of Newcastle etc., 1855
Artist, Willm. Weir, 26 Clayton Street East.
(
www.historicaldirectories.org )
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Also on not-art angle, Stephen's son/William's brother, Joseph was according to 1861 census ( 3816-19-32) a "fuse packer".
Lord Armstrong's world renowned munitions factory was closeby in Elswick!
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Michael Dixon
Newcastle